Factual Knowledge is knowledge that is basic to specific disciplines. This dimension refers to essential facts, terminology, details or elements students must know or be familiar with in order to understand a discipline or solve a problem in it. (Bloom's Taxonomy)
Knowledge of terminology
Knowledge of specific details and elements
The National Mathematics Advisory Panel states that learning mathematics requires three types of knowledge:
Factual knowledge and automatic retrieval of basic math facts refers to having ready in memory the answers to a relatively small set of problems of addition, subtraction, multiplication and division.
Facility in using mathematics, or reasoning about mathematical situations, depends on mathematical knowledge and familiarity with mathematical concepts. The more relevant knowledge a student is able to recall and the wider the range of concepts he or she has understood, the greater the potential for engaging a wide range of problem-solving situations and for developing mathematical understanding. Without access to a knowledge base that enables easy recall of the language and basic facts and conventions of number, symbolic representation, and spatial relations, students would find purposeful mathematical thinking impossible. Facts encompass the factual knowledge that provides the basic language of mathematics, and the essential mathematical facts and properties that form the foundation for mathematical thought. Procedures form a bridge between more basic knowledge and the use of mathematics for solving routine problems, especially those encountered by many people in their daily lives. In essence a fluent use of procedures entails recall of sets of actions and how to carry them out. Students need to be efficient and accurate in using a variety of computational procedures and tools. They need to see that particular procedures can be used to solve entire classes of problems, not just individual problems. Knowledge of concepts enables students to make connections between elements of knowledge that, at best, would otherwise be retained as isolated facts. It allows them to make extensions beyond their existing knowledge, judge the validity of mathematical statements and methods, and create mathematical representations.
This cognitive process covers the following behaviours:
1. Recall
Recall definitions, terminology, number properties, geometric properties and notation.
2. Recognize
Recognize mathematical objects, shapes, numbers and expressions. Recognize mathematical entities that are mathematically equivalent.
3. Compute
Carry out procedures for + , , , ÷ , or a combination of these with rational numbers, radicals, powers and polynomials. Approximate numbers to estimate computations. Carry out routine algebraic procedures. Compute %, factorize, and add hours in a time chart.
4. Retrieve
Retrieve information from graphs, tables or other sources; read simple scales.
5. Measure
Use measuring instruments; use units of measurement appropriately; estimate measures; convert units (imperial SI) in one dimension; and express total time worked in decimal form and in hours and minutes.
6. Classify/Order
Classify/group objects, shapes, numbers and expressions according to common properties; make correct decisions about class membership; and order numbers and objects by attributes.
The National Mathematics Advisory Panel states that learning mathematics requires three types of knowledge:
Factual knowledge and automatic retrieval of basic math facts refers to having ready in memory the answers to a relatively small set of problems of addition, subtraction, multiplication and division.
Factual Knowledge
https://www.bced.gov.bc.ca/exams/specs/grade10/fmp/10_cognitive_processes.pdf
Facility in using mathematics, or reasoning about mathematical situations, depends on mathematical knowledge and familiarity with mathematical concepts. The more relevant knowledge a student is able to recall and the wider the range of concepts he or she has understood, the greater the potential for engaging a wide range of problem-solving situations and for developing mathematical understanding. Without access to a knowledge base that enables easy recall of the language and basic facts and conventions of number, symbolic representation, and spatial relations, students would find purposeful mathematical thinking impossible. Facts encompass the factual knowledge that provides the basic language of mathematics, and the essential mathematical facts and properties that form the foundation for mathematical thought. Procedures form a bridge between more basic knowledge and the use of mathematics for solving routine problems, especially those encountered by many people in their daily lives. In essence a fluent use of procedures entails recall of sets of actions and how to carry them out. Students need to be efficient and accurate in using a variety of computational procedures and tools. They need to see that particular procedures can be used to solve entire classes of problems, not just individual problems. Knowledge of concepts enables students to make connections between elements of knowledge that, at best, would otherwise be retained as isolated facts. It allows them to make extensions beyond their existing knowledge, judge the validity of mathematical statements and methods, and create mathematical representations.
This cognitive process covers the following behaviours:
1. Recall
Recall definitions, terminology, number properties, geometric properties and notation.
2. Recognize
Recognize mathematical objects, shapes, numbers and expressions. Recognize mathematical entities that are mathematically equivalent.
3. Compute
Carry out procedures for + , , , ÷ , or a combination of these with rational numbers, radicals, powers and polynomials. Approximate numbers to estimate computations. Carry out routine algebraic procedures. Compute %, factorize, and add hours in a time chart.
4. Retrieve
Retrieve information from graphs, tables or other sources; read simple scales.
5. Measure
Use measuring instruments; use units of measurement appropriately; estimate measures; convert units (imperial SI) in one dimension; and express total time worked in decimal form and in hours and minutes.
6. Classify/Order
Classify/group objects, shapes, numbers and expressions according to common properties; make correct decisions about class membership; and order numbers and objects by attributes.
Adapted from “Mathematics Cognitive Domain”. TIMSS 2007 Mathematics Framework [http://timss.bc.edu/timss2007/PDF/T07_AF_chapter1.pdf]